Maths Olympiad Sample Paper 2 (Practice)

Maths Olympiad topic 33: Maths Olympiad mock test 2 · Set 28 · 40 questions

How to solve it (Name the topic, then solve): Name the topic first: angles, counting, worst case, probability, digits, mensuration, data, coordinates, AP, algebra, primes or Venn diagrams. Use that lesson’s method; draw a quick sketch, list or Venn diagram on rough paper. Rule out options of the wrong kind — a probability above 1, or a triangle angle of 180° or more. Check by working backwards or with a second method when you can.

1. 1.A drawer has lots of red, black, yellow, white and blue socks, all mixed up. In the dark, how many socks must you take out to be sure of getting a matching pair? (a) 10 (b) 6 (c) 2 (d) 5
2. 2.What is the sum of all the whole numbers from 1 to 96? (a) 4608 (b) 4656 (c) 9312 (d) 4560
3. 3.How many times is the digit 7 written when you write all the numbers from 1 to 39? (a) 3 (b) 4 (c) 2 (d) 5
4. 4.What is the mode of 10, 8, 8, 3, 19, 8 and 3? (a) 8 (b) 19 (c) 10 (d) 3
5. 5.In an isosceles triangle, the two equal angles are 25° each. What is the third angle? (a) 65° (b) 155° (c) 130° (d) 25°
6. 6.A bag has 5 blue balls and 6 green balls. Without looking, how many balls must you take out to be sure of getting at least one ball of each colour? (a) 7 (b) 2 (c) 6 (d) 11
7. 7.In a class of 37 children, 19 like mangoes, 27 like bananas and 3 like neither. How many like both? (a) 9 (b) 34 (c) 3 (d) 12
8. 8.In how many different ways can the letters of the word SUN be arranged? (a) 6 (b) 9 (c) 3 (d) 12
9. 9.What is the missing term in the AP 12, 19, ?, 33, 40? (a) 25 (b) 27 (c) 33 (d) 26
10. 10.In a class of 45 children, 29 like cricket, 23 like football and 9 like both. How many like at least one of the two? (a) 52 (b) 45 (c) 43 (d) 34
11. 11.In which quadrant does the point (−1, −7) lie? (a) Second quadrant (b) Fourth quadrant (c) First quadrant (d) Third quadrant
12. 12.What is the 30th term of the AP 5, 11, 17, 23, …? (a) 180 (b) 179 (c) 174 (d) 185
13. 13.A book has 225 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 567 (b) 568 (c) 558 (d) 450
14. 14.Two angles of a triangle are 65° and 85°. What is the exterior angle at the third corner? (a) 30° (b) 150° (c) 95° (d) 115°
15. 15.Using (a + b)² = a² + 2ab + b², what is 101²? (a) 10201 (b) 10211 (c) 9801 (d) 10001
16. 16.A bag has 5 blue, 3 white and 8 green balls. One ball is taken out without looking. What is the probability that it is green? (a) 1/2 (b) 1/3 (c) 9/16 (d) 1/16
17. 17.How many times is the digit 6 written when you write all the numbers from 1 to 89? (a) 8 (b) 20 (c) 19 (d) 18
18. 18.In an isosceles triangle, the two equal angles are 75° each. What is the third angle? (a) 75° (b) 105° (c) 15° (d) 30°
19. 19.How many two-digit numbers have digits that add up to 4? (a) 4 (b) 10 (c) 3 (d) 5
20. 20.A captain and a vice-captain are to be chosen from 10 players. In how many ways can this be done? (a) 20 (b) 45 (c) 100 (d) 90
21. 21.How many factors does 108 have? (a) 10 (b) 12 (c) 11 (d) 13
22. 22.Which is the correct factorisation of x² + 16x + 63? (a) (x − 7)(x − 9) (b) (x + 1)(x + 63) (c) (x + 1)(x + 15) (d) (x + 7)(x + 9)
23. 23.A bag has 3 blue balls and 4 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 4 (b) 7 (c) 2 (d) 5
24. 24.In a class of 27 children, 11 like mangoes, 9 like bananas and 3 like both. How many like at least one of the two? (a) 20 (b) 14 (c) 27 (d) 17
25. 25.A book has 108 pages, numbered 1, 2, 3 and so on. How many digits are printed to number all the pages? (a) 217 (b) 324 (c) 207 (d) 216
26. 26.A bag has 2 blue, 3 yellow and 9 white balls. One ball is taken out without looking. What is the probability that it is white? (a) 9/14 (b) 5/7 (c) 5/14 (d) 1/3
27. 27.Two angles of a triangle are 35° and 70°. What is the third angle? (a) 145° (b) 105° (c) 75° (d) 110°
28. 28.A bag has 5 black balls and 11 yellow balls. Without looking, how many balls must you take out to be sure of getting 2 yellow balls? (a) 16 (b) 6 (c) 7 (d) 2
29. 29.13 friends meet and each one shakes hands once with every other friend. How many handshakes are there? (a) 169 (b) 156 (c) 78 (d) 91
30. 30.What is the area of a circle of diameter 14 cm? (Use π = 22/7.) (a) 154 sq cm (b) 77 sq cm (c) 616 sq cm (d) 44 sq cm
31. 31.A fair dice is rolled once. What is the probability of getting a number greater than 4? (a) 1/6 (b) 1/2 (c) 1/3 (d) 2/3
32. 32.How many times is the digit 9 written when you write all the numbers from 1 to 95? (a) 9 (b) 15 (c) 13 (d) 16
33. 33.How many prime numbers are there between 40 and 70? (a) 6 (b) 8 (c) 9 (d) 7
34. 34.What is the 27th term of the AP 19, 24, 29, 34, …? (a) 130 (b) 154 (c) 135 (d) 149
35. 35.In an isosceles triangle, the angle between the two equal sides is 150°. What is each of the other two angles? (a) 15° (b) 25° (c) 150° (d) 30°
36. 36.In a class of 26 children, 13 like maths, 14 like science and 2 like both. How many like at least one of the two? (a) 27 (b) 26 (c) 25 (d) 23
37. 37.A fair dice is rolled once. What is the probability of getting a number less than 2? (a) 1/5 (b) 1/3 (c) 5/6 (d) 1/6
38. 38.What is the midpoint of the line joining (8, 20) and (20, 10)? (a) (15, 14) (b) (6, 5) (c) (14, 15) (d) (28, 30)
39. 39.In a class of 46 children, 26 like tea, 22 like coffee and 6 like both. How many like at least one of the two? (a) 36 (b) 48 (c) 46 (d) 42
40. 40.A bag has 12 black balls and 7 white balls. Without looking, how many balls must you take out to be sure of getting 2 white balls? (a) 2 (b) 14 (c) 19 (d) 13

Free maths olympiad lessons, practice and worksheets at talentjr.in/maths-olympiad